A bag contains N balls out of which 3 are whi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given that there are $3$ white,$6$ green,and $(N-9)$ blue balls in a bag of $N$ balls.The probability of drawing a white ball first,a green ball s

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(D) Given that there are $3$ white,$6$ green,and $(N-9)$ blue balls in a bag of $N$ balls.The probability of drawing a white ball first,a green ball second,and a blue ball third without replacement is:$P(W_1 \cap G_2 \cap B_3) = P(W_1) 	imes P(G_2 \mid W_1) 	imes P(B_3 \mid W_1 \cap G_2)$We are given $P(W_1 \cap G_2 \cap B_3) = \frac{2}{5N}$ and $P(B_3 \mid W_1 \cap G_2) = \frac{2}{9}$.Substituting the values:$P(W_1) = \frac{3}{N}$$P(G_2 \mid W_1) = \frac{6}{N-1}$$P(B_3 \mid W_1 \cap G_2) = \frac{N-9}{N-2}$Thus,$\frac{3}{N} 	imes \frac{6}{N-1} 	imes \frac{N-9}{N-2} = \frac{2}{5N}$.Also,from the definition of conditional probability:$P(B_3 \mid W_1 \cap G_2) = \frac{N-9}{N-2} = \frac{2}{9}$.Solving for $N$:$9(N-9) = 2(N-2)$$9N - 81 = 2N - 4$$7N = 77$$N = 11$.

Similar Questions

Let $X$ and $Y$ be two events of a sample space such that $P(X)=\frac{1}{3}$,$P(X|Y)=\frac{1}{2}$ and $P(Y|X)=\frac{2}{5}$,then which of the following is true?

$A$ fair die is rolled. Consider events $E=\{1,3,5\}, F=\{2,3\},$ and $G=\{2,3,4,5\}$. Find $P((E \cup F) | G)$ and $P((E \cap F) | G)$.

Let $E^c$ denote the complement of an event $E$. Let $E, F, G$ be pairwise independent events with $P(G)>0$ and $P(E \cap F \cap G) = 0$. Then $P(E^c \cap F^c \mid G)$ equals

If $A$ and $B$ are two events of a random experiment such that $P(A)=0.6$,$P(B)=0.3$,and $P(A \mid B)=0.5$,then $P(\bar{B} \mid \bar{A})=$

Given that the two numbers appearing on throwing two dice are different,find the probability of the event 'the sum of numbers on the dice is $4$.'

Vedclass Test Series

Exam Paper Generator

Online Exam Module